Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+6y &= -6 \\ 7x-5y &= -3\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $7x = 5y-3$ Divide both sides by $7$ to isolate $x$ $x = {\dfrac{5}{7}y - \dfrac{3}{7}}$ Substitute this expression for $x$ in the first equation. $-6({\dfrac{5}{7}y - \dfrac{3}{7}}) + 6y = -6$ $-\dfrac{30}{7}y + \dfrac{18}{7} + 6y = -6$ Simplify by combining terms, then solve for $y$ $\dfrac{12}{7}y + \dfrac{18}{7} = -6$ $\dfrac{12}{7}y = -\dfrac{60}{7}$ $y = -5$ Substitute $-5$ for $y$ in the top equation. $-6x+6( -5) = -6$ $-6x-30 = -6$ $-6x = 24$ $x = -4$ The solution is $\enspace x = -4, \enspace y = -5$.